By National Semiconductor Application Note 1126 2003

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**Extra info for BGA (Ball Grid Array) **

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A second similar layer B may be added by placing each sphere of B in contact with three spheres of the bottom layer, at positions B in Fig. 32. This arrangement has the lowest energy and is therefore stable. A third layer may be added in two different ways. third layer C are added over the holes in the first layer A that are not occupied by B, as in Fig. 32. We obtain the hexagonal close-packed structure (Fig. 33) when the spheres in the third layer are placed directly over the centers of the spheres in the first layer, thus replicating layer A.

Example of (a) two-dimensional lattice, (b)pattern, and (c) two-dimensional crystal illustrating a pattern associated with each lattice point. A lattice can be represented by a set of translation vectors as shown in the two-dimensional (vectors a', ) and three-dimensional lattices (vectors z , g, 2 ) in Fig. 5(a) and Fig. 6, respectively. The lattice is invariant after translations through any of these vectors or any sum of an integer number of these vectors. When an origin point is chosen at a lattice point, the position of all the lattice points can be determined by a vector which is the sum of integer numbers of translation vectors.

6, respectively. The lattice is invariant after translations through any of these vectors or any sum of an integer number of these vectors. When an origin point is chosen at a lattice point, the position of all the lattice points can be determined by a vector which is the sum of integer numbers of translation vectors. In other words, any lattice point can generally be represented by a vector such that: + Eq. 1 ) - R = n,; + n,b + n,;, n,,,,, = 0,f l,f2 ,... a,;, where ct are the chosen translation vectors and the numerical coefficients are integers.